Question

Two parallelograms have pairs of sides that are 3 feet long and 2 feet long. One of the parallelograms is a rectangle and the other is not. Which has a bigger area, and why

Answer 1

draw the two figures, and draw a diagonal in each one.

have you seen a formula to find the area of a triangle if you have 2 sides and the angle between them given?
it is : Area = (1/2)(side1)(side2)(sin(angle between them))

for the rectangle
Area = 2(1/2)(2)(3)sin90
=6(1) = 6

now we know that sin(any angle in a triangle) is a number between 0 and 1
and it reaches 1 only for sin 90º

so if the angle is any other than 90, either acute or obtuse, sin(angle) has to be < 1
so the area = 2(1/2)(2)(3)(a number less than 1)
so clearly the area on the non-rectangle has to be less than 6